Correlation coefficient

correlation coefficient definition

Correlation coefficient is a quantity that measures the strength of the association (or dependence) between two variables (x and y). For example if we are interested to know whether there is a relationship between the heights of fathers and son, a correlation coefficient can be calculated.

There are different correlation coefficients :

  • Pearson r : linear dependence
  • Kendall tau : rank-based correlation coefficient
  • Spearman rho : rank-base correlation coefficient

Pearson correlation is the most used one.

correlation formula is described here.

Negative and positive correlation

The value of correlation coefficient can be negative or positive and it is comprised between -1 and 1 (see the plots below).

correlation coefficient -1correlation coefficient -1correlation coefficient -1

  • -1 means strong negative correlation : In this case y decreases when x increases (left panel figure)
  • 0 means that there is no relationship between the two variables (x and y) (middle panel figure)
  • 1 means strong positive correlation : In this case y increases when y increases (right panel figure)

Correlation coefficient calculator

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